Calibration of measurement tools and scientific instrumentation typically involves the use of another tool that has a higher degree of precision than the tool(s) or instrument(s) to be calibrated. Using such a “reference”, “standard” or “gold standard” tool of higher precision, measurements taken by the tool or instrument to be calibrated can be compared with measurements of the reference tool that has a higher degree of precision, and adjusted accordingly, to match the measurements of the higher precision tool as closely as possible. This not only increases the precision of each tool or instrument compared to and adjusted according to the reference tool, but it also standardizes the measurements of the tools and instruments so adjusted, so that they produce measurement results similarly to one another. However, for tools and instruments on the cutting edge of the limits of precision, this approach is no longer possible, since a tool having greater precision does not exist, and therefore some other technique, tool and/or method is needed to calibrate such tools and instruments. This need arises, among other areas, in areas where the discipline requires the ability to measure smaller and smaller units, such as distance, volume, or other unit of measurement, as the discipline progresses over time. Examples of such disciplines include semiconductor technologies, such as VLSI design and manufacturing, transistor design and manufacturing etc. A discipline that has been immediately faced with such need is the field of nanotechnology.
Nano-machines are typically at the limits of technology with regard to the units of measurement that can be detected and worked with by such machines. Therefore, it is impossible to provide a “reference” tool of the type described above, that could be used to calibrate such nano-machines.
An example of a conventional self-calibration technique useful for improving accuracy in the alignment of masks used in making integrated circuits via electron beam lithography is disclosed in U.S. Pat. No. 4,583,298 to Raugh, which is incorporated herein, in its entirety, by reference thereto. Raugh uses the concept of symmetry to calibrate a rigid plate by first placing the rigid plate in a reference orientation and measuring the locations of points in a grid on the calibration plate to establish reference measurements. After that, the rigid plate is repositioned into “non-reference” orientations, and for each non-reference orientation, the locations of the points in the grid are again measured. A calibration map is used to determine calibrated measured values for each orientation for each grid point. Numerical values are then set for parameters to minimize deviation from the congruence of each orientation of the rigid plate with all other orientations measured. Raugh determined that single or multiple rotations of the rigid plate about a single point cannot give complete self-calibration, since a rotationally symmetric distortion would look the same in all rotated orientations, and therefore would not be detectable as an error. The same holds for translations which, alone, are ineffective in identifying translationally invariant distortions. However, using rotational displacement of the rigid plate and a translation displacement, or another rotation about a different point, makes it possible to self-calibrate according to Raugh's technique.
Ye et al., in U.S. Pat. No. 5,798,947, which is incorporated herein in its entirety, by reference thereto, also addresses self-calibration of lithography stages. A mapping of a two-dimensional array of stage positions to corresponding positions in a Cartesian coordinate grid is made to determine distortion therebetween. The mapping function is performed by a series of orthogonal Fourier series functions to decouple the determination of a pivoting point and a rotation angle from the determination of the distortion function. An operation is performed to determine complete non-four-fold rotationally symmetric distortion between the two-dimensional array of stage positions and the Cartesian coordinate grid from measured locations of marks in an original orientation to locations having been rotated by ninety degrees. A translation operation is also performed to take further distortion measurements and to determine incomplete non-four-fold rotationally symmetric distortion.
However, when applying the above self-calibration techniques, the rotations and translations required introduce errors themselves, as the amount of rotation and/or translation is not exact at the level of precision of the tool. Therefore replicate symmetry operations of the object in the input field of the tool are required to reduce error of its mean symmetrical locations. The object must span the entire input field of the tool to assure complete calibration. This is a requirement that must be met by Design Of Experiments (DOE) in order to leverage all possibilities of the domain of the application, wherein, in this case, the domain is the device input field for machines.